Week 14 - Homework

\(H_o\) : \(\alpha_i = 0\)

\(H_a\) \(\alpha_i \neq 0\)

\(H_o\) : \(\sigma^2_{\beta} = 0\)

\(H_a\) \(\sigma^2_{\beta} \neq 0\)

Machine <-c(rep(1,8),rep(2,8),rep(3,8))
Spindle <- rep(c(rep(1,4),rep(2,4)),3)
Obs<-c(12,9,11,12,8,9,10,8,14,15,13,14,12,10,11,13,14,10,12,11,16,15,15,14)
Table<-data.frame(Machine,Spindle,Obs)

Machine<-as.fixed(Machine)
Spindle<-as.random(Spindle)

#Spindle Nested with Machine
model<-lm(Obs~Machine+Spindle%in%Machine)
gad(model)

## Analysis of Variance Table
## 
## Response: Obs
##                 Df Sum Sq Mean Sq F value    Pr(>F)    
## Machine          2  55.75 27.8750  1.9114 0.2915630    
## Machine:Spindle  3  43.75 14.5833  9.9057 0.0004428 ***
## Residual        18  26.50  1.4722                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The p value (0.2915630) for factor A, the machine is greater than \(\alpha =0.05\). Therefore we fail to reject the null hypothesis. However, the p value for factor B (0.0004428), the nested factor, the spindle, is less than \(\alpha =0.05\) so we reject the null hypothesis for factor B and say that the Spindle nested in the Machine is significant.